Séminaire régulier IUSTI – 24 juin 2019 – 11h salle 250
Direct Numerical Simulation of Pore-Scale Turbulence: Multiscale Statistics and Upscaling
Sourabh V. Apte – Oregon State Univ., ÉU
Turbulent flows in porous media occur in a wide variety of applications, from catalysis in packed beds to heat exchange in nuclear reactor vessels. In this talk, we will review some of the recent developments in characterizing turbulence in porous media and using the data to develop volume averaged, upscaled models. The porescale flow physics, which are important to properties such as bulk mixing performance and permeability, are investigated in detail using direct numerical simulation (DNS) through a periodic face centered cubic (FCC) unit cell, covering inertial through fully turbulent regime. This low porosity arrangement of spheres is characterized by rapid flow expansions and contractions, and results an early onset to turbulence. The simulations are performed using a fictitious domain approach [Apte et al, J. Comp. Physics 2009], which uses non-body conforming Cartesian grids, with very high resolution. Results are used to investigate the structure of turbulence in the Eulerian and Lagrangian frames, the distribution and budget of turbulent kinetic energy, and the characteristics of vorticity and helicity distribution in complex packed beds. In addition, Lagrangian statistics of scale dependent curvature angle are calculated by tracking a large number of fluid particle trajectories and compared with homogeneous, isotropic turbulence to understand the effects of flow confinement on turbulence in porous media. A Monte-Carlo based stochastic model to predict the long-time behavior of curvature angles is developed and shown to correctly predict the asymptotic behavior as obtained from DNS. Finally, the porescale data is used to close a spatially-averaged upscaled model. A Darcy-Forchheimer type law is derived, and a prior computation of the permeability and Forchheimer coefficient are presented and compared with existing data.